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Central charges and RG flow of strongly-coupled N=2 theory

Dan Xie, Peng Zhao

TL;DR

The paper develops a systematic framework to compute the central charges $a$, $c$, and the flavor central charge $k_G$ for a broad class of 4d N=2 SCFTs engineered from the 6d $(2,0)$ theory via regular and irregular punctures. By leveraging topological twisting, ’t Hooft anomaly matching, Seiberg-Witten data, and, where available, 3d mirror symmetry, it provides explicit expressions for central charges across several families of Argyres-Douglas theories, including $I_{k,N}$, $II_{k,N}$, Type III/IV degenerations, and their regular puncture augmentations. The authors also study RG flows between AD theories, showing that $a$ decreases along these flows in agreement with the $a$-theorem, and they illustrate minimal flows via Newton-polygon arguments. The work yields both new explicit central-charge results and a cohesive picture linking geometric data, spectra, and anomalies in strongly coupled 4d theories, with implications for holography and BPS spectra. Potential extensions include gravity duals, other $(2,0)$/$(D_N)$ constructions, and deeper investigations of the $R(B)$ function and its relation to BPS states.

Abstract

We calculate the central charges a, c and k_G of a large class of four-dimensional N=2 superconformal field theories arising from compactifying the six-dimensional N=(2,0) theory on a Riemann surface with regular and irregular punctures. We also study the renormalization group flows between the general Argyres-Douglas theories, which all agree with the a-theorem.

Central charges and RG flow of strongly-coupled N=2 theory

TL;DR

The paper develops a systematic framework to compute the central charges , , and the flavor central charge for a broad class of 4d N=2 SCFTs engineered from the 6d theory via regular and irregular punctures. By leveraging topological twisting, ’t Hooft anomaly matching, Seiberg-Witten data, and, where available, 3d mirror symmetry, it provides explicit expressions for central charges across several families of Argyres-Douglas theories, including , , Type III/IV degenerations, and their regular puncture augmentations. The authors also study RG flows between AD theories, showing that decreases along these flows in agreement with the -theorem, and they illustrate minimal flows via Newton-polygon arguments. The work yields both new explicit central-charge results and a cohesive picture linking geometric data, spectra, and anomalies in strongly coupled 4d theories, with implications for holography and BPS spectra. Potential extensions include gravity duals, other / constructions, and deeper investigations of the function and its relation to BPS states.

Abstract

We calculate the central charges a, c and k_G of a large class of four-dimensional N=2 superconformal field theories arising from compactifying the six-dimensional N=(2,0) theory on a Riemann surface with regular and irregular punctures. We also study the renormalization group flows between the general Argyres-Douglas theories, which all agree with the a-theorem.

Paper Structure

This paper contains 21 sections, 85 equations, 18 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Central charge $a,c$
  3. Summary of calculation tools
  4. Regular punctures
  5. Example 1:
  6. Example 2:
  7. Irregular punctures: general Argyres-Douglas theories
  8. $\hbox{I}_{k,N}$ theory: $(A_{k-1}, A_{N-1})$ theory
  9. $\hbox{II}_{k,N}$ theory
  10. Type III theory: degenerating case
  11. Example 3:
  12. Type IV theory
  13. $(\hbox{I}_{k,N},F)$ theory:
  14. $(\text{I}_{k,N},S)$ theory:
  15. $(\hbox{II}_{k,N},S)$ and $(\hbox{II}_{k,N},F)$ theory:
  16. ...and 6 more sections

Figures (18)

  • Figure 1: The calculation of the central charges uses the weakly-coupled Lagrangian descriptions: a) $S$-duality, b) UV completion, c) 3d mirror.
  • Figure 2: 3d mirror for the $T_{3}$ theory
  • Figure 3: Quiver tail for a regular puncture in the mirror theory.
  • Figure 4: Gaiotto construction of superconformal QCD with $N_{f} = 4$ and $N_{f} = 6$ on a sphere with four punctures, and their mirror pairs. One can find that the true flavor symmetry is $U(2N_f)$ and $U(1)$, since there is a chain of $A_{2N_f}$ subquiver which satisfies the 4d $\mathcal{N}=2$ conformal relation, which will give the $U(2N_f)$ symmetry.
  • Figure 5: 3d mirror for the $T_{k}$ theory.
  • ...and 13 more figures